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I need help evaluating the integral Cotx^{3}/10

I factored out the 1/10 from the integral and am just left with (1/10)*Cotx^{3}

from here i do not really know what to do. I rewrote it in terms of sine and cosine to get

(1/10)*(Cosx^{3}/Sinx^{3})dx

I multiply the integral by (1/Sinx^{3}) to get rid of the denominator and am left with

(1/10)*(Cosx^{3}dx

I factor out a (Cosx^{2}) and am left with

(1/10)*(Cosx^{2})(Cosx)dx

Rewriting using trig indentities, I get

(1/10)*(1-Sinx^{2})(Cosx)dx

rewriting i get

(1/10)*(cosx-sinx^{2}cosx)dx

I solve this integral and get

(1/10)sinx - (1/10)*((sinx)^{3}/3) + C

but that is incorrect. The answer is supposed to be

(-1/20)cotx^{2}-(1/10)ln(sinx)+C

What went wrong?

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# Homework Help: Integrals involving trig functions

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